Although holographic complexity has been extensively studied, it's still an open problem to define complexity appropriately. One of the main approach to define complexity is Nielsen's geometric approach [1]}, [2]}, called complexity geometry. In the geometric way to define complexity, the complexity is defined as the path length on the unitary group or Hilbert space, so a proper distance function is required. Various distance functions are proposed [2]}, [4]}, [5]}, [6]}, but the physical meaning of these distance functions is not clear enough.
